Problem: Solve for $x$ and $y$ using substitution. ${-3x-y = 7}$ ${y = 5x+1}$
Solution: Since $y$ has already been solved for, substitute $5x+1$ for $y$ in the first equation. ${-3x - }{(5x+1)}{= 7}$ Simplify and solve for $x$ $-3x-5x - 1 = 7$ $-8x-1 = 7$ $-8x-1{+1} = 7{+1}$ $-8x = 8$ $\dfrac{-8x}{{-8}} = \dfrac{8}{{-8}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = 5x+1}\thinspace$ to find $y$ ${y = 5}{(-1)}{ + 1}$ $y = -5 + 1$ $y = -4$ You can also plug ${x = -1}$ into $\thinspace {-3x-y = 7}\thinspace$ and get the same answer for $y$ : ${-3}{(-1)}{ - y = 7}$ ${y = -4}$